The bound state solution of the radial Schrödinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary ℓ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different n and ℓ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around 56 Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained by Gamow code for ℓ = 0.

PoS(BORMIO2017)015NURE: An ERC project to study nuclear reactions for neutrinoless double beta decay M. Cavallaro 2 Neutrinoless double beta decay (0νββ) is considered the best potential resource to determine the absolute neutrino mass scale. Moreover, if observed, it will signal that the total lepton number is not conserved and neutrinos are their own anti-particles. Presently, this physics case is one of the most important research "beyond Standard Model" and might guide the way towards a Grand Unified Theory of fundamental interactions.Since the ββ decay process involves nuclei, its analysis necessarily implies nuclear structure issues. The 0νββ decay rate can be expressed as a product of independent factors: the phase-space factors, the nuclear matrix elements (NME) and a function of the masses of the neutrino species. Thus the knowledge of the NME can give information on the neutrino mass scale, if the 0νββ decay rate is measured.In the NURE project, supported by a Starting Grant of the European Research Council, nuclear reactions of double charge-exchange (DCE) will be used as a tool to extract information on the ββ NME. In DCE reactions and ββ decay, the initial and final nuclear states are the same and the transition operators have similar structure. Thus the measurement of the DCE absolute crosssections can give crucial information on ββ matrix elements. IntroductionDouble charge-exchange reactions (DCE) are processes characterized by the transfer of two units of the isospin component (two protons transformed into two neutrons or vice versa), leaving the mass number unchanged. The initial and final nuclear states involved in DCE reaction and ββ decay are the same and the transfer operators have similar spin-isospin mathematical structure. Namely they both contain a Fermi, a Gamow-Teller and a rank-two tensor term. A relevant amount of linear momentum (of the order of 100 MeV/c) is available in the virtual intermediate channel in both processes. This is a crucial similarity since the nuclear matrix elements strongly depend on the momentum transfer and other processes (single charge-exchange reactions, 2νββ decay etc.) cannot probe this feature. Thus, even if the two processes are mediated by different interactions, the involved nuclear matrix elements could be connected and the determination of the DCE reaction cross-sections could give important information on the ββ matrix elements.One should remind that a proportionality relation is well established at a level of few percent between single β decay strengths and single charge-exchange reaction cross-sections, under specific dynamical conditions. Indeed, single charge-exchange reactions are routinely used as a tool to determine Fermi and Gamow-Teller transition strengths for single β decay, as demonstrated by several works [1][2][3][4][5][6][7]. However, studying the link between ββ-decay strengths and DCE crosssections is a not trivial task and requires a strong effort.Experimental attempts were done in the past to perform DCE reactions [8], [9]. Howeve...

No abstract